First of all, you were right about the meaning of 澀, it was kinda "negative", basically is the taste/feeling that your tongue feels when you eat grapes or drink red wine. Some people might like it, but in general, it is not considered positive. Also, in Cantonese, when you say X得起, it means you can afford the consequence by doing X, for example, ...
calling your lemon tea as astringent in taste would be a little bit bad for business
well, the logic of such saying is, let’s say:
1 teabag is for 300ml hot water, for brewing a cup of tea
if someone want to save the cost, using 900ml hot water for 1 tea bag, one would get 3 cups of tea. and, the tea would not astringent 🙀
so, when a manufacturer claimed ...
Lemon usually tastes 酸澀 - tartness/acerbity, a sharp sour taste that is rough and bitter and tends to stick to your teeth and tongue.
This is a frequently employed tactic in advertising - use a distasteful thing to induce the notice and curiosity of the buying crowd, and make up a slogan around the taste to challenge the customer's guts to give it a try, and ...
澀 here refers to 苦澀 (bitter)
澀得起，就係我 means "Can afford to taste bitter, that's me"
(We know how much bitterness is appropriate in lemon tea)
A lot of popular food and drink contains bitterness, the most famous ones being coffee and beer, so are tea and lemon. Bitterness is a part of these food and drink's charm
The other name for 苦瓜 (bitter melon) ...
There's this blog post: 《澀得起》, which explains:
Perhaps as a translation we could opt for something like: tangy!
The writer of the blog post ends by saying:
No matter how sour it is - you'll be able to take it.